Irrelivant foreword in italicised text: I am often reluctant to tell people about my projects untill they are done, otherwise I feel like I'm letting them down when it doesn't work or I don't finish it because I'm distracted by another project, but in this case I've decided "**** it" and I'm going to tell you that I'm working on a synthesizer (mostly analog) because I am confounded and have a deadline.

I've been looking up circuits and chips for a voltage controlled filter, found a great chip: the lm13700, a transconductance op-amp, looks like it will do the job just fine but if you have any suggestions please make them

However, when researching circuits used by synthesizers, they allways seem to have multiple stages in the filter; all the same and all controled by the same control voltage.

One-half of an LM13700 makes an extremely simple 1st-order lowpass filter (like one resistor feeding one capacitor to ground) that has a very gradual slope that is nearly useless. Additional stages are added to increase the slope so it is useable as a filter. That was about 35 years ago.

Lately (for about 15 years) a switched-capacitor lowpass filter IC is used that has two 4th-order or one 8th-order lowpass stages with very sharp slopes.

Thankyou for that little explanation, I suspected it may be something like that, it all makes sense now! And thanks the info about the switched capacitor filter too, however I'm going to stick with the 35 year old tech as that is what I was aiming for ye olde synthesizer.

Please define what you mean by 4th order and 8th order stages.
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The order of the filter determines the steepness of the rolloff outside the passband which is one measure of the "goodness" of the filter. Each order adds 6dB/octave, thus 1st order is 6db/octave, 2nd order is 12dB/octave, 3rd order is 18dB/octave, etc.

If you simply add single-order filters in series then they load each other down and the response will be terribly droopy. A filter IC IC that is designed with many orders has opamps with positive feedback to boost the response at the cutoff frequency so the overall response is a very sharp Butterworth.

If you are intending to build a VCF for a musical synthesiser, then although the details that Audio Guru has described will be required, to get decent reuslts there will be a bit more to it.
35 years ago, the problems were solved with special filter chips, designed for musical syntheseiser use - like the SSM2040 for example: http://datasheets.me/datasheets/73312/data-SSM2040.html

They included exponential voltage control, to allow the filter to 'track' easily.

You won't find them very easily these days, I'm afraid, they're pretty rare -although I believe there maybe some Hong Kong 'clones' available, but the data sheet should give an idea of what is required.
Trying to get LM13700s to work in the same way might be a bit of a challenge, without the exponential converter.

Another option might be to look to copy a Moog filter?
Bob Moog created a superbly musical 24dB/octave low pass filter for his famous Minimoog, using discrete components.
See here:

Why is the exponential converter required? what would it do? and without it what would happen?

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Traditionally, analogue music synthesizers use a linear voltage control, usually calibrated for 1 volt per octave. This allows the potential divider (resistor chain!), derived via the key contacts, to use same value resistors throughout, making it much easier to construct. Each musical octave needs to be divided into 12 semitones, which would mean a change of 83mV per semitone (1/12)

Unfortunately, musical semitone frequencies don't correspond to a linear scale, they need to 'track' to a logarthmic scale.
So you need a 'linear to log' (exponential) conversion process to get the linear key voltages to track the oscillators (and filter cutoff frequency) in a logarithmic way.
It just so happens that if you increase the Vbe of a transistor operating in it's linear range by, in this case, 83mV, you effectively double the collector current. Another 83mV increase, another doubling of collector current. Nice simple linear to log converter?

Well, yes and no. The stability of this particular characteristic of a transistor is also very temperature sensitive. Which is why some of the older analogue synths went out of tune so easily, if the ambient temperature moved by even a small amount. It can mean quite elaborate temperature compensation techniques need to be applied, to make a reasonably stable working version of this type of linear/log converter.
There is a pretty good analysis of the concept here

Of course, while this kind of conversion needs to be very accurate for the oscillators (VCOs) of the synth, you might get away with less accurate tracking for the filters. But they need to 'track' reasonably well, to maintain the same filter characteristics over the keyboard range.
And if you intend your filter to oscillate - or operated in the very high 'Q' (resonance) region, then it must track pretty well.

Which is why it was so much easier when people, like SSM, did all the hard work inside the chip......

That was brilliant thankyou! I spent about an hour reading things on that website I'll be going back to it agian, thankyou, I find it easier to understand than other explanations I have read on other websites.

P.S. I got the thing about the 83.33333333mV per semitone, but overlooked the exponential nature of the musical scale.

There is a schematic at the end of the manual, and of course much of the earlier description refers to that overall schematic.

One thing about that schematic is that it's easy to check out how that circuit actually sounds. There are loads of Moog Prodigy videos on You tube - including this one: http://www.youtube.com/watch?v=hExz24-jTBU which I made to show all the features on my own Moog working well, before I sold it.

The section from 3:13 is the first section about the VCF, while the bit from 4:05 shows the filter in oscillation - this is where good exponential 'tracking' is vital!

It is also interesting to note that the Prodigy was one model where Moog made use of the heated chip option for thermal stability. (This, you might recall, was one of the options discussed in that link I referred to on my earlier post).
I can confirm it works pretty well. Although it usually took about 5 minutes for the synth tuning to 'stabilise' after switching on, it was pretty good after that.

Unfortunately, although these thermal problems are a bit of a nuisance, there's really no getting away from them, if you want to 'go analogue' with your synth....

I've been reading loads of his website but I have a few problems with it which when combined make it really hard for me to follow what he's talking about. I have a non standard screen configuaration, and his webpage has a fixed width, even after zooming out to the last readable zoom, the text and images are still cut off, I find myself sticking the whole page in notepad and looking at the images alone. that combined witha dash of autism and the way he describes things* just makes it a tad too difficult to understand without spending a whole bloody day reading it!

*(UA-3 is conected to UA-2 and as you can see it's configured in an exponentional frangooglier with R13098476 connecting transcuberumbly to UC-2 acting on T-5 and UC-4 as a trubliator)
That sort of thing, which I keep running into in his descriptions, is the least accessible explanation possible for me.